Examples of processes where the entropy increases

When the number of product molecules is higher than the number of reactant molecules: More individual particles means more available microstates.

When a compound changes from solid to liquid state: A molecule in a liquid state has many more possible ways to orient itself (more available microstates) than a molecule which is locked in the crystal lattice of a solid.

When a compound changes from liquid to gaseous state: A molecule in a gaseous state has even more possible ways to orient itself (more available microstates) than a molecule in a liquid state.

When two miscible liquids are mixed: It is similar to the expansion of a gas into an empty container. The number of microstates available to an evenly distributed mixture is so much higher than if the two liquids were to stay separated.